The main difference I see though is that since Mastodon provides RSS feeds, I could at least follow the feed of my country's emergency services without needing a specialised app.
Given the general trust in American corporations, it's not absurd to think some of the 89% of the population that doesn't use Twitter would be more willing to install an application to follow official communication on Mastodon than to use Twitter.
Anyway warnings are just broadcast on the mobile network here, which works fine.
That can only be described as a loss.
One would likely just subscribe to your city's hashtag for large cities or to your town hall's account for small ones, and that's all. The rest works like Twitter (except there is less risk of important posts getting invisibilised by the feed algorithm).
In my fediverse test, I just subscribed to #Antwerpen (as well as #Antwerp and #Anvers but that's a whole other problem...) and I did get relevant and interesting posts. In their small town my parents are subscribed to the town hall's Facebook account (the only reason they signed up to Facebook) and it would work the same on any other app, except it likely would spy on them a bit less. Mastodon's Android app is not a "more custom" app than Twitter or Facebook's apps are, on the contrary I would argue.
I just can't get used to checking this thing more than once every few days and like Twitter it just doesn't work if you're not constantly reading your feed, because then you're missing most posts.
It's called a website.
It's hard to answer this question without knowing your local city. My town of < 5000 people has the appropriate .gov site set up and maintained; it's one of the responsibilities of the local government. I'd imagine that any local government structure large enough to have evacuation plans in place is also large enough to have a website to communicate those plans on...
This was especially useful for things like transit, or emergency situations. If there was a snowstorm, I would check the BC transit Twitter account. When there was an active shooter at my university, I checked the Ottawa RCMP Twitter account.
And I relayed that information to others, including people like you, making sure that even if you don't have Twitter you had the latest information. Now, Twitter can't be relied on for the latest information anymore. Government websites are not real time. There were millions of people using Twitter for this, and now they're no longer going to use the platform. This is absolutely a loss for the platform, no two ways about it.
If it federated with Mastadon (or was a Mastadon instance) then others could seamlessly pull those official comms into their feed without having to ever navigate to the platform. Or, for those of us that don't care to have a centralized feed, we could just go to the instance directly for government comms. No more of this "get nagged by twitter ads while I try to read updates from my local government".